The Collaborative International Dictionary of English v.0.48:

Rigidity \Ri*gid"i*ty\, n. [L. rigiditas: cf. F. rigidit['e].
   See Rigid.]
   1. The quality or state of being rigid; want of pliability;
      the quality of resisting change of form; the amount of
      resistance with which a body opposes change of form; --
      opposed to flexibility, ductility, malleability, and
      softness.
      [1913 Webster]

   2. Stiffness of appearance or manner; want of ease or
      elegance. --Sir H. Wotton.
      [1913 Webster]

   3. Severity; rigor. [Obs. orR.] --Bp. Burnet.
      [1913 Webster]

   Syn: Stiffness; rigidness; inflexibility.
        [1913 Webster]

WordNet (r) 3.0 (2006):

rigidity
    n 1: the physical property of being stiff and resisting bending
         [syn: rigidity, rigidness]
    2: the quality of being rigid and rigorously severe [syn:
       inflexibility, rigidity, rigidness] [ant:
       flexibility, flexibleness]

Moby Thesaurus II by Grady Ward, 1.0:

128 Moby Thesaurus words for "rigidity":
   abidingness, absoluteness, accuracy, adamantness,
   attention to fact, care for truth, changelessness, concentration,
   constancy, correctness, delicacy, dourness, durability,
   durableness, duration, endurance, exactitude, exactness,
   faithfulness, faultlessness, fidelity, fineness, firmness,
   firmness of mind, fixedness, flawlessness, flintiness, frozenness,
   fundamentalism, grimness, hard-bittenness, hard-nosedness,
   hardening, hardness, immobility, immobilization, immovability,
   immovableness, immutability, implacability, impliability,
   inelasticity, inertia, inexorability, inextricability,
   inflexibility, intransigeance, intransigence, intransigency,
   intransigentism, invariability, invariableness, inveteracy,
   irreconcilability, irremovability, lastingness, literalism,
   literality, literalness, long standing, loyalty,
   mathematical precision, meticulousness, niceness, nicety, obduracy,
   obdurateness, obstinacy, orthodoxy, perfection, permanence,
   permanency, perpetualness, persistence, persistency, preciseness,
   precisianism, precision, purism, puritanism, quiescence,
   refinement, relentlessness, renitence, renitency, right, rightness,
   rigidness, rigor, rigorism, rigorousness, settledness, severity,
   solidity, stability, standing, starchiness, stasis, staunchness,
   steadfastness, steadiness, steeliness, sternness, stiff temper,
   stiffness, strictness, stubbornness, subtlety, tautness, tenseness,
   tension, tensity, textualism, the letter, tightness, torpor,
   toughness, trueness, unalterability, unbendingness,
   unchangeability, unchangingness, uncompromisingness, ungivingness,
   unmovability, unrelentingness, unyieldingness, vis inertiae